The present disclosure relates to thermal imaging. More particularly, the present disclosure relates to the nondestructive characterization of objects and materials.
The science of diffusion waves has been a focus of intense interest since the middle of the 19th century [1-3]. However, it is the latest four decades that witnessed rapid growth in this parabolic-wave-governed energy or matter transport research which encompasses several sub-disciplines such as thermal waves, diffuse photon density waves, and excited-carrier plasma waves [4-7]. In contrast to electromagnetic or acoustic waves which are described in terms of hyperbolic differential equations, diffusion waves lack wave fronts and are reflection- and refraction-less in nature [8]. Thermodynamically, diffusion occurs to minimize the free energy of a system and should be driven by a free energy gradient. Detection of distance-integrated, rather than localized, distributions of energy is a unique characteristic of diffusion-wave fields. An important feature of the physics of parabolic diffusion wave fields, both stationary and drifting, is that an energy preserving completeness relation linking the time-domain propagation of a diffusive energy impulse with a complete stationary frequency spectrum cannot be defined due to the strongly lossy character of energy migration across the contributing frequency modes. As a consequence of the loss of frequency modes, non-localization and spreading of diffusive impulses occurs at the expense of coherence between time and depth of energy propagation, leading to poor axial resolution which deteriorates with time and distance from the source and is a serious limiting factor of diffusion waves. Historically, the first attempt for localizing energy in a thermal-wave field was made by using pseudorandom binary sequence (PRBS) optical excitation followed by cross-correlation signal processing [9]. Later, the frequency modulated (FM) time delay technique was proven to have faster response and improved dynamic range compared to the PRBS scheme [10]. Significant progress in this area was made with the attainment of binary-phase-coded thermal coherence tomography (TCT) [11]. The energy localization achieved in TCT, although incomplete, enables the deconvolution of thermal responses from axially discrete sources and improves the depth resolution in thermal-diffusion wave imaging. All these methods make use of matched filtering using pulse compression, which is a traditional radar technique for enhancing range resolution and signal to-noise ratio (SNR) [12] in a hyperbolic wave field. Here, the coded signal can be described by the frequency response H(ω) of the coding filter. The frequency response of the matched filter which receives the signal is the complex conjugate H*(ω) of the coding filter response. The output of the matched filter is the inverse Fourier transform of the product of the signal spectrum and the matched filter response:
                              y          ⁡                      (            t            )                          =                              1                          2              ⁢              π                                ⁢                                    ∫                              -                ∞                            ∞                        ⁢                                                                                                  H                    ⁡                                          (                      ω                      )                                                                                        2                            ⁢                              ⅇ                                  ⅈ                  ⁢                                                                          ⁢                  ω                  ⁢                                                                          ⁢                  t                                            ⁢                                                          ⁢                              ⅆ                ω                                                                        (        1        )            
Compared to harmonic signals, the definite advantage of a short pulse capable of maintaining flat power spectrum over a very broad bandwidth, even under diffusive attenuation losses, recently inspired the present inventors to introduce the chirped-pulse thermal-diffusion-wave radar [13]. The advantages of highly compressed output with negligible side-lobe power distribution led to much improved SNR and depth profiling capability that make this concept particularly attractive for the optothermal analysis of biological samples in which infrared absorption by water molecules and the maximum permissible exposure (MPE) ceiling [14] on the excitation fluence appreciably limit the measurable thermal-diffusion-wave signal. However, in the case of diffusion waves, the limited frequency bandwidth afforded by this coding and its inability to encompass widely varying frequency contents as time evolves and spatial coordinates change, lead to incomplete or limited localization and loss of coherence on timescales and associated spatial locations outside the completeness bandwidth. Poor efficiency or SNR and the lack of control over axial resolution, which in turn hinders the three-dimensional visualization of subsurface features, are shortcomings of these radar approaches and they are major impediments in thermal-diffusion-wave applications to systems with intricate or complex subsurface structures such as biological specimens.